Geometry and measures worksheet — GCSE Foundation

1.A gardener wants to plant a tree so that it is the same distance from two straight garden walls that meet at a corner, and also the same distance from two ornamental posts standing 4 m apart. Which construction locates this point?

2.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

3.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

4.Write down the exact value of tan 45°.

5.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.

6.A triangular bunting flag has two equal sides. The angle between those two equal sides is 80°, and the other two angles of the flag are equal to each other. Work out the size of each of the two equal angles.

7.Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. The hypotenuse of triangle ABC equals the hypotenuse of triangle DEF, and side AB equals side DE. Which condition proves that the two triangles are congruent?

8.A cylindrical tin has a curved surface, a flat circular base and a flat circular lid. A label is stuck around the curved surface only. How many of the tin's faces are NOT covered by the label?

9.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.

10.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

11.Which of the following correctly describes what it means for two lines to be perpendicular?

12.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.

13.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.

14.A hexagonal prism lies on a table. A flat cut is made straight across it, at right angles to its length (so the cut is parallel to the two identical end faces). What shape is the cross-section?

15.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.